The present invention relates generally to the process of satellite orbit determination, that is, the estimation of orbits of spacecraft or other objects relative to primary celestial bodies, given applicable measurements. In particular, the invention relates to a highly refined orbit determination process comprising a novel synthesis of old and new methods useful in solving existing and new problems in orbit determination.
Orbit determination refers to the estimation of orbits of spacecraft (or natural satellites or binary stars) relative to primary celestial bodies, given applicable measurements. All useful orbit determination methods produce orbit estimates, and all orbit estimates have errors. Minimizing these errors is desirable in all cases.
Orbit determination methods are distinguished with three categories according to their inputs, outputs, and accuracy performance:
(1) Initial orbit determination (IOD)
(2) Batch least squares differential corrections (LS)
(3) Sequential processing (SP)
Operationally, the order in which these methods are used defines a dependency tree: IOD output is LS input, and LS output is SP input:
xe2x80x83IODLSSP
For accuracy performance: IOD produces crude orbit estimates, LS produces refined orbit estimates in a batch processing mode, and SP produces refined orbit estimates in a sequential mode.
IOD methods input tracking measurements with tracking platform locations, and output spacecraft position and velocity estimates. No a priori orbit estimate is required. IOD methods are characterized by the use of approximations and/or recursive algorithms operating on nonlinear two-body dynamics. IOD methods were derived by various authors: LaPlace, Gauss, Lagrange, Lambert, Gibbs, Herrick, Williams, Stumpp, Lancaster, Blanchard, Gooding, and Smith. Operationally, the orbit determination process is frequently begun, or restarted, with IOD.
LS methods input tracking measurements with tracking platform locations and an a priori orbit estimate, and output a refined orbit estimate. An a priori orbit estimate is required. Associated output error magnitudes are small when compared to IOD outputs. LS methods use a sequence of linear LS corrections where sequence convergeance is defined as a function of tracking measurement residual RMS (Root Mean Square). Each linear LS correction is characterized by a minimization of the sum of squares of tracking measurement residuals. LS methods produce refined orbit estimates in a batch mode, together with error covariance matrices that are optimistic; i.e., orbit element error variances are typically too small by at least an order of magnitude. Operationally, LS may be the only method used, or it may be used to initialize SP. LS methods frequently require inspection and manual measurement editing by human intervention. LS algorithms therefore require elaborate software mechanisms for measurement editing. The LS method was derived first by Gauss in 1795, and later independently by Legendre. Gauss published in Latin, after Legendre. Gauss"" English translation was first available in 1857.
SP methods input tracking measurements with tracking platform locations, input an a priori state estimate (inclusive of orbit estimate), and input an a priori state error covariance matrix. An a priori state estimate is required, and an a priori state error covariance matrix is required. SP methods output refined state estimates in a sequential mode. SP filter methods are forward-time recursive sequential machines using a repeating pattern of filter time update of the state estimate and filter measurement update of the state estimate. The filter time update propagates the state estimate forward, and the filter measurement update incorporates the next measurement. The recursive pattern includes an important interval of filter initialization. SP smoother methods are backward-time recursive sequential machines using a repeating pattern of state estimate refinement using filter outputs and backwards transition. Time transitions for both filter and smoother are dominated most significantly by numerical orbit propagators. The search for sequential processing was begun by Wiener, Kalman, Bucy, Meditch, and others.
In summary, IOD methods produce crude state estimates from measurements alone, whereas LS and SP methods produce refined corrections to a priori state estimates.
Current orbit determination methods suffer from a number of deficiencies. Current methods limit the number of spacecraft orbits in their simultaneous state estimate and are constrained to particular constellations of spacecraft orbits. Current methods require the user to specify the state estimate structure (and, in the case of sequential methods, an error covariance matrix), which burdens the user with a task he may not be qualified, or may not wish, to perform. Additionally, current methods lack the ability to estimate atmospheric density in real time using an SP method and fail to employ the variation of parameters in universal variables. Another deficiency of current methods is that they fail to provide a measurement simulator that employs the same stochastic sequence models as those used by the optimal sequential filter for time updates.
To overcome the shortcomings of prior approaches to orbit determination, a method and apparatus are needed that utilize stochastic sequence models and real-time data range and tracking data to produce accurate orbital estimates. Additionally, such method and apparatus would also use the range and tracking data in conjunction with near-time atmospheric density data to produce a real-time estimate of local atmospheric density and to correct orbit determinations from error relating to atmospheric drag.
Such a system of orbit determination would take advantage of object oriented programming in high order languages, such as C++, in particular the containers and methods made available in the Standard Template Library (STL).
An embodiment of the present invention is a method for estimating the orbits of a satellite or a constellation of satellites using stochastic sequence models and real-time data.
It is an aspect of the present invention to provide a method and apparatus that implements a system of orbit determination that enables the user to specify an arbitrary number of satellite orbits, of arbitrary types, to be included in the simultaneous state estimate structure.
It is a further aspect of the present invention to provide a method and apparatus that implements a system of orbit determination that includes an automatic definition algorithm of the state estimate structure for an orbit determination, given appropriate six-dimensional orbit definitions and other user inputs.
It is a further aspect of the present invention to provide a method and apparatus that implements a system of orbit determination that has the ability to estimate atmospheric density in real time, either on a local scale or a global scale, using a sequential processing method.
It is a further aspect of the present invention to provide a method and apparatus that implements a system of orbit determination that uses variation of parameters in universal variables for orbit propagation.
It is a further aspect of the present invention to provide a method and apparatus that implements a system of orbit determination that has a measurement simulator that employs the same stochastic sequence models used by the optimal sequential filter for time updates.
It is a further aspect of the present invention to provide a method and apparatus that implements a system of orbit determination using object oriented programming in a high order language, such as C++, making particular use of containers and methods provided by the Standard Template Library (STL).
These and other objectives of the present invention will become apparent from a review of the general and detailed descriptions that follow. An embodiment of the present invention is a method for estimating the orbits of a satellite or a constellation of satellites using physics, optimal estimation theory and algorithms derived therefrom, and tracking dataxe2x80x94either real time, near real time, or archived.